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PROCEEDINGS, Thirty-Seventh Workshop on Geothermal Reservoir Engineering
Stanford University, Stanford, California, January 30 - February 1, 2012
SGP-TR-194
ASSISTED IGNITION OF HYDROTHERMAL FLAMES IN A HYDROTHERMAL
SPALLATION DRILLING PILOT PLANT
P.STATHOPOULOS, T.ROTHENFLUH, M.SCHULER, D.BRKIC, Ph.RUDOLF VON ROHR
ETH Zürich – Department of Mechanical Engineering – Institute of Process Engineering
Sonneggstrasse 3
Zurich, CH-8092, Switzerland
e-mail: [email protected]
ABSTRACT
Spallation drilling is a promising drilling technique
that could prove to be economically advantageous
over rotary techniques for deep wells needed e.g. for
geothermal energy production. It takes advantage of
the properties of certain rock types, to spall rock to
small disk-like fragments due to thermal stresses. In
water-filled boreholes two to three kilometers deep,
water exceeds its critical pressure and hydrothermal
flames can provide the required heat to spall the rock.
One potential spallation drilling head consists of a
combustion chamber fed by water, fuel and oxidant.
The reactants are preheated and react to a
supercritical, hydrothermal flame in the aqueous
environment of the burning chamber. The water in
the combustion chamber reaches high temperatures
and exits through a nozzle together with the
combustion products. The resulting supercritical
water jet is directed to the rock surface to induce
fragmentation.
Building on the investigations on hydrothermal
flames carried out in our lab for almost two decades,
the work presented in this paper focuses on the
assisted ignition of these flames. For the
investigation of spallation drilling, a novel
hydrothermal spallation drilling pilot plant was built.
The self-ignition methodology used in all the
previously published investigations is not an option
anymore, due to safety reasons. Additionally, the
assisted ignition of a hydrothermal flame is relevant
for the field application of the technique, where the
flame has to be ignited in a deep borehole. The
implemented ignition set-up, an ignition model and
the corresponding experimental results are presented.
INTRODUCTION
If geothermal power utilization for energy production
is to become competitive in a large energy production
scale, the drilling costs need to be reduced. These
costs, for conventional - rotary drilling increase
exponentially with depth (Tester 2007). Spallation
rock drilling (Rauenzahn 1989) is based on the rapid
local heating of rock inducing high thermal stresses
on its surface due to its low thermal conductivity.
The heat flux required to fracture the rock can be
provided by high velocity flame jets impinging on the
rock surface. For the concept to work in deep well
drilling, a flame ignited in a high-density water-based
drilling fluid at hydrostatic pressures exceeding the
critical pressure of water (220.6 bar) should be used.
An approach for the application of this technique,
currently under investigation in our laboratory, is
called "hydrothermal spallation drilling" (Augustine
2009). Although the drilling concept has been well
documented, many critical issues for its
implementation in deep boreholes are still open. The
most important relevant scientific topics, which are
being investigated in our research group, are
presented on Fig.1.
Figure 1: Scientific topics investigated in our
research group
Although research on hydrothermal flames in
supercritical water (SCW) is carried out the last three
decades, no systematic solution of the assisted
ignition of such a flame has been presented so far.
This work intends to fill this gap and propose a
reliable method of assisted ignition, which could be
also implemented in a real borehole.
IGNITION METHODOLOGY - MODELLING
There are many different methodologies to ignite a
combustible mixture, two of which are the most used,
namely spark ignition and ignition on a hot surface.
The first is used in internal combustion engines,
while the second is implemented in gas furnaces.
Both methodologies are well known, but could not be
directly implemented in the application in question,
due to the high density aqueous environment
prevailing in flames in SCW, and due to the
respective high pressures.
Hot surface ignition has been chosen as the most
easily applicable in the aforementioned environment.
An electrical resistance could be heated up with DC
or AC voltage and heating powers up to one kW
could be easily reached if necessary.
Adapting existing literature models on the specific
conditions of our ignition setting we attempt to
understand the underlying mechanisms of the
phenomenon and predict the parameters necessary for
ignition. Among the existing models in the literature,
the model presented from Adomeit (Adomeit 1961),
which is based on the theoretical models of
F.Kamenetskii (A.Frank-Kamenetskii 1969), has
been chosen as a first approximation. The model
predicts the surface temperature and the heat flux to a
fluid necessary for the ignition of combustible
mixtures, flowing over hot surfaces, as sketched in
Fig.2.
Figure 2 Ignition model after Adomeit (Adomeit
1961).
A fluid with a velocity U∞ flows over a surface,
which is kept at constant temperature Tw. In steady
state conditions a temperature boundary layer (profile
T(x)) develops in the perpendicular direction to the
wall, and a qualitative picture of its temperature
profile is presented Fig.2 for the cases with and
without an exothermic reaction. Hence it is expected
that the highest temperatures in the flow will be
located inside its boundary layer and therefore the
ignition conditions will be reached within this layer.
Several simplifications are made to reduce the
complexity of the problem, the most important of
which are:
The pre-ignition temperature rise is small in
comparison to the temperature value at the
heated wall. This assumption implies that
RT<<E, in the computational field, where R,
is the universal gas constant, E the activation
energy of the combustion reaction
(assuming one step Arrhenius kinetics) and
T is the temperature in K.
The reaction rate depends only on
temperature of the gas. The dependence on
the concentration and on pressure is
neglected.
The average temperature between the bulk
and the wall is used for the calculation of the
material properties.
The approach in the current work considers only the
boundary layer, whose thickness of which is
estimated from the value L/Nu, where “L” is the
length of the igniter and Nu is the Nusselt number of
the flow. Because the thickness of the boundary layer
is much smaller than the length of the igniter, the
geometry of the problem is approximated from a gas
flowing between two parallel plates, which are at
constant temperatures, Tw and T∞. Heat transfer takes
place only through heat conduction between these
walls, and the convection comes into play only
through the definition of the distance between the
layers. The temperature distribution in this thermal
boundary layer can be calculated from the energy
balance equation for this layer. Based on the
assumption that ignition takes place when no solution
for the temperature distribution can be found, the
critical ignition conditions are calculated.
The energy conservation equation in this gas layer
can be written as:
(1)
And the corresponding boundary conditions are:
For , (2)
, (3)
In equations 1-3, λ is the thermal conductivity of the
gas, Q is the heat of combustion of the gas, C is a
constant for the reaction, R is the universal gas
constant, E is the activation energy of the reaction,
and T is the temperature of the system in K, Tw is the
wall temperature, T∞ is the free stream temperature
and Nu is the Nusselt number of the flow.
Since the length of the cylinder is much higher than
the thickness of the boundary layer, one can simplify
the problem further in a one dimensional heat
conduction problem. Expressing the equations in a
dimensionless form and simplifying the exponential
part of the right hand side of the equation according
to F.Kamenetskii (A.Frank-Kamenetskii 1969), we
come up with the following non-linear boundary
conditions problem:
(4)
with boundary conditions:
(5)
(6)
The dimensionless parameters for equations 4-6 are
presented on table 1.
Table 1 Dimensionless parameters of the problem.
Parameter Definition
Dimensionless
Temperature
( )
Dimensionless
Distance
Frank
Kamenetskii
parameter
(
)
The boundary conditions problem 4-6 can be solved
analytically as shown from F. Kamenetskii (A.Frank-
Kamenetskii 1969), leading to an expression of the
temperature distribution in the computational field in
question. The solution expressed as a function of two
integration constants is:
( √ )
(7)
The integration constants “a” and “b” should be
calculated from the boundary conditions of the
problem (eq.(5) &(6)).
From eq.(5) we calculate the value of “b” as:
√ (8)
Using the boundary condition (6) and substituting “b”
from (8), we come up with an equation for the
calculation of “ ” as a function of the system
parameters “ ” and “ ”.
{ √
√ }
(9)
Depending of the boundary conditions and the
material properties, equation (9) can have three, two,
one or no solution for the integration constant “ ”.
As Adomeit (Adomeit 1961) shows, the case where
eq.(9) has only one solution corresponds to the
ignition conditions of the mixture and the critical
value of parameter “ ”, which leads to ignition, is
the solution of eq.(10).
√
√
√
√
(10)
Eq. (10) has to be solved numerically. From the value
of “ ”, calculated from eq. (10), one can calculate the
critical value of the parameter “ ” and through its
definition the ignition wall temperature value for a
given Nusselt number or the critical value of the
Nusselt number for a given wall temperature.
CONVECTIVE HEAT TRANSFER
COEFFICIENT MEASUREMENTS
Motivation - Goal
The boundary conditions and the computational field
of the presented ignition model are defined from the
convective heat transfer coefficient of the flow.
Since no data can be found in the literature for the
heat transfer coefficient of the flow in the burner
setup of the plant, the actual heat transfer coefficient
had to be measured prior to making any prediction
for the ignition conditions.
The heat transfer experiments had the goal to define
the average convective heat transfer coefficient “h”
over the surface of an igniter.
Measurement concept
From the definition of the convective heat transfer
coefficient in eq. (11), one has to measure the
exchanged heat flux between a surface and a fluid,
the bulk temperature of the fluid and the surface
temperature, in order to measure the heat transfer
coefficient as a product variable.
( ) (11)
Since the experiments are conducted in a high
pressure vessel with limited space, a simple
experimental setup is designed to provide as much
data as possible.
A K-type thermocouple with a 3mm diameter was
used for the bulk temperature measurement, while the
heat flux was calculated from the voltage and current
values fed to the igniter. The direct measurement of
the surface temperature was more challenging,
because it is technically impossible to attach a
thermocouple on a heated surface at temperatures
between 350-800°C in desalinated water. This
problem was solved by the implementation of a
ceramic igniter made of silicon nitride, which had a
favorable temperature dependence of its resistance.
Calculating the resistance through measurement of
the voltage and current values fed to the igniter, the
average temperature of its heated length could be
estimated.
Experimental Setup
Spallation drilling pilot plant - short description
The presented experiments were conducted in the
new hydrothermal spallation drilling plant of our lab.
The plant is using water-ethanol mixtures as a fuel
and pure oxygen as an oxidation medium and is
capable of reaching fuel power 120 kW. Its
maximum working pressure is 350bar and it is
designed to process rock probes with a diameter of
9.5cm and a length of 35 cm. The reactants are
preheated at temperatures reaching 420 °C, prior to
their injection in the pressure vessel of the plant. Two
high pressure water pumps provide the cooling water.
Core of the plant is its high pressure burning
chamber, where all experiments are carried out. It has
a volume of approximately 5.8 liters, and it was
designed to withstand pressures of 600bar at wall
temperatures of 500°C. Its inner diameter is 14cm
and the length of its inner space is 40 cm. Optical
access to the vessel is provided by two small sapphire
windows on its head. Probe access and positioning,
while under pressure, is achieved with two individual
positioning devices similar to the ones presented by
Prikopsky (Prikopsky 2007), the positioning accuracy
of which is 0.2mm.
The experiments presented in the current work
concentrate on the heat transfer conditions prevailing
in the burner setup of the plant. A technical drawing
of the upper part of the burning chamber is presented
on Fig.3.
Figure 3 Technical drawing of the upper part of the
used pressure vessel
The inner space of the pressure vessel is divided in
the outer cooling mantle, where water keeps the load-
bearing walls at low temperatures, and the inner
space where the hydrothermal flame will be ignited at
its upper part and the rock probes will be inserted
from below in the future. The cooling mantle is fed
with water from two inlet holes (not shown on Fig.3)
and water is provided to the inner space with two
holes opposite to one another, in order to provide a
homogeneous cooling to the burner of the setup.
The pre-heated fuel mixture is fed axially to the
burning chamber through a specially designed burner
nozzle. Oxygen is fed from a radial hole (not shown
on Fig.3) with an angle to the axis of the vessel equal
to 45°, and then through the annulus between the
burner nozzle and the reactor body.
A detailed drawing of the burning chamber with its
dimensions and the operational data used during the
experiments is presented on Fig.4.
Figure 4 Measurement setup with operational and
the dimensional data (dimensions are given in mm)
Igniter characteristics
The igniter used as a heated surface is a cylindrical
body consisting primarily of silicon nitride. The
electrical resistance is implemented in the main body
by a sintering procedure and it consists of 80% vol.
silicon nitride and the rest is additives, MoSi2 and
TaN. The outer surface of the igniter was electrically
insulating.
The total length of the igniter is 90 mm, the diameter
of its heated zone is 4mm and its length is 40mm.
The dependence of its resistance from its temperature
was calibrated in a high temperature oven up to
temperatures of 520 °C.
The temperature in the calibration experiments was
measured with two K-type thermocouples positioned
near the igniter and its resistance was measured with
a multi-meter. The accuracy of the thermocouple
measurement was ±1.5°C, and of the multi-meter
0.8% of the measured value.
The calibration line is presented on Fig.5, together
with its confidence intervals, computed based on the
orthogonal regression method (Gillard 2009).
Technical reasons did not allow for the calibration of
the igniter at higher temperatures (the material used
for soldering its electrical contacts melted above
550°C), but calibration data provided from the
construction company show a linear dependency up
to temperatures of 1000°C (Bach 2011).
The electrical connection system was custom made
and it is a combination of a ceramic capillary,
through which the bear wires were inserted for the
high temperature region and kapton insulated copper
wires for the low temperature region. The resistance
of the feeding line was subtracted from the total
resistance measurements, in order to account only for
the igniter resistance.
Figure 5 Igniter Calibration Curve. Confidence
interval ±0.5%.
The igniter can be fed with voltage values up to 230V
and current values up to 9A depending on its
resistance.
Experimental procedure
As already mentioned the heat transfer measurements
will be the input for the ignition model, with the aim
to predict the ignition conditions in the system in
question. For this reason experimental conditions
were chosen which simulate the ignition experiments
planned for the future. Accordingly, measurements
were performed with both fuel and gas streams
(nitrogen).
All the measurements were performed at a constant
pressure of 260±4 bar and the fluids were preheated
at temperatures between 350 and 420°C. Four fuel-
stream compositions were used having
0%,10%,20%,30% wt. ethanol, and various mass-
flow values for nitrogen, in order to investigate its
influence. The mass flows used are presented in table
2.
Table 2 Fuel and gas steam mass flows and
compositions used in the experiments
Fuel steam
composition
[wt.% Ethanol]
Mass flows
Fuel stream
[kghr-1
]
Nitrogen
stream
[Nlmin-1
]
0
10
130 20
30
40
10
10
130 20
30
40
20
10 130
20
30 180
35 220
30
10 130
15
20 180
25 220
It must be stressed that the experiments in question
are performed in a pressure and temperature region
crossing the critical point of the mixtures used
(Abdurashidova 2007), (Wagner 2008) (Japas 1985).
In this region the material properties (especially the
cp and Pr values) exhibit a very strong dependency on
the pressure and the temperature. Due to this material
behavior, the convective heat transfer coefficient
depends not only on the flow conditions, but it is also
a strong function of the temperature of the fluid, the
applied heat flux and the presence of buoyancy
effects (Pioro 2005), (Polyakov 1991).
For this reason the same experiments were carried
out for two heat flux values, namely 0.5 and 0.7
MWm-2
.
The procedure implemented for each measurement
consisted of the following steps:
Once the predefined fluid temperature and
fluid mass flow was reached, voltage was
fed to the igniter.
A defined ramp was followed for each
measurement leading to the first heat flux
value (see Fig.6).
This value of the voltage was kept constant
for sixty seconds and the voltage value, the
current value and the bulk temperature were
recorded.
The next step in the voltage was adjusted to
reach the second value of the heat flux on
the igniter (see Fig.6).
After the sixty seconds of the second heat
flux measurement a ramp was followed for
the reduction of the voltage on the igniter.
Once the voltage was switched off, the bulk
temperature was recorded for sixty seconds.
Figure 6 Voltage ramps example for a measurement.
Experimental results
The results for two mass flows of the 10%wt. ethanol
fuel mixture are presented on Fig.7 and Fig.8 for two
heat flux values (0.5 and 0.7 MWm-2
respectively). In
these experiments the mass flow of nitrogen was kept
constant at 130 Nlmin-1
.
Figure 7 Convective heat transfer coefficient values
for a mixture of water, ethanol (10%wt.) and
nitrogen (mf – fuel mixture flow rate; mN2 - nitrogen
flow rate).Heat flux from the heated surface to the
flow 0.5[MWm-2
].
From the data presented in Fig.7 and Fig.8 it can be
clearly seen, that the addition of nitrogen reduces the
heat transfer coefficient of the flow.
Another significant result is that for all the cases a
peak of the heat transfer coefficient is observed.
Similar effects were reported in many publications,
investigating the heat transfer coefficient of a
supercritical water flow in a pipe (Jäger 2011). The
reason for such a peak is the very strong change in
the fluid properties. This peak gives also an
indication for the pseudo critical temperature (the
temperature at which the cp acquires its maximum
value) of the ternary mixture under the reported
conditions. Unfortunately the bulk temperature
resolution of our measurements does not allow for
the accurate measurement of this temperature.
According to the values presented from Rogak
(Rogak 2001) for water – oxygen systems, the
addition of nitrogen should lower the pseudo critical
temperature of the working fluid in a similar manner
with the one observed in our measurements.
Nevertheless in our case we have a water-ethanol
mixture and we can only assume its pseudo critical
temperature from the data of its critical temperature
presented from Abduraslidova (Abdurashidova
2007).
Figure 8 Convective heat transfer coefficient values
for a mixture of water, ethanol (10%wt.) and
nitrogen (mf – fuel mixture flow rate; mN2 - nitrogen
flow rate).Heat flux from the heated surface to the
flow 0.7[MWm-2
].
Moreover we are investigating mixtures which are
highly non-ideal and the data presented are only
indications that our mixture behaves in the same way.
Unfortunately there are no data for the ternary
mixture we are using at the present, and the only way
to interpret the results is through the material
properties presented in the works of Abduraslidova
(Abdurashidova 2007), and Japas (Japas 1985).
Another expected observation was the dependency of
the heat transfer coefficient on the heat flux used in
the heated surface. The heat transfer coefficient falls
as the heat flux from the surface to the fluid is
increased.
The same results as for Fig.7 and Fig.8 are shown for
a 30%wt. ethanol fuel mixture on Fig.9 and Fig.10. In
these experiments the mass flow of nitrogen was
adjusted to a value corresponding to oxygen - fuel
combustion equivalence ratio of 1.2. This value was
180 Nlmin-1
for a fuel mass flow 20 kghr-1
and 220
Nlmin-1
for a fuel mass flow 25 kghr-1
. The heat flux
values used were the same as in the previous
diagrams.
Comparing these diagrams with the ones on Fig.7 and
Fig. 8, one can see that the bulk temperature, at
which the peak of the heat transfer coefficient is
observed, shifts to lower values. This is an additional
indication that the behavior the water-oxygen
mixtures described from Rogak (Rogak 2001) is
similar with the ternary mixture in our case.
Figure 9 Convective heat transfer coefficient values
for a mixture of water, ethanol (30%wt.) and
nitrogen (mf – fuel mixture flow rate; mN2 - nitrogen
flow rate).Heat flux from the heated surface to the
flow 0.5[MWm-2
].
Figure 10 Convective heat transfer coefficient values
for a mixture of water, ethanol (30%wt.) and
nitrogen (mf – fuel mixture flow rate; mN2 - nitrogen
flow rate).Heat flux from the heated surface to the
flow 0.7 [MWm-2
].
Error calculation-uncertainty estimation
The uncertainty of the measurements was calculated
by using simple Gaussian error propagation for each
product variable. The directly measured variables
were the voltage and the current on the igniter, and
the bulk temperature. The accuracy of the voltage and
current measurements was 0.75 V and 50 mA
respectively. Hence the resistance measurement error
was calculated from eq.(12).
√(
)
(
)
(12)
The value of the surface temperature was measured
from the inverse regression line, resulted from the
calibration procedure of the igniter eq. (13).
(13)
The error of the regression variables (b0 and b1) was
calculated from the error-in-variables orthogonal
regression procedure presented in the work of Gillard
(Gillard 2009). The error of the temperature
measurements was calculated from eq. (14).
√(
)
( )
((
) )
(14)
The value of the heat transfer coefficient was
calculated from eq. (15).
(15)
From eq. (15) it can be seen, that the accuracy of the
heat transfer coefficient measurement depends
strongly on the temperature difference between the
wall and the bulk of the fluid. This is the reason why
the measurements with the lower heat flux values
have a higher measurement error.
IGNITION CONDITIONS PREDICTION
Based on the heat transfer coefficient measurements
presented in the previous section, a calculation of the
ignition conditions is performed. The calculated cases
will be some of the target cases for the first ignition
experiments, which will be carried out in our lab.
The simple ignition model presented in the respective
section is herewith implemented, with the following
computational assumptions:
The fluid properties are evaluated for the
average temperature between the bulk and
the wall temperature. Mole averaged values
are taken for the mixture, based on
properties tables of each component (NIST
Chemistry WebBook 2012).
The molecular values of thermal
conductivity and viscosity are taken.
The values for the activation energy “E” and
the pre-exponential factor are taken form the
work of Mercadier (Mercadier 2007).
The value of the measured bulk temperature
will be used as T∞ for the model.
Additionally, only the cases were taken into
consideration, where a homogeneous mixture is
expected. The model assumes a homogeneous
mixture for the calculations, and in the experiments
in question this is the case for temperature values
above the critical point of the fuel stream.
Accordingly only the bulk temperatures above 350°C
were considered.
Fig. 11 and 12 present two curves for two different
values of the mass flow. The composition of the fuel
stream is in both cases 10%wt. and the gas mass flow
is the same as in the heat transfer experiments.
Figure 11. Values of the modeled ignition wall
temperature (red) and the igniter temperature (blue)
for two cases with 10%wt. ethanol in the fuel stream
and 0,5 [MWm-2
] heat flux from the igniter.
The red curves show the critical ignition wall
temperature values calculated from the model for the
corresponding bulk temperatures in the y-axis. The
blue lines are the wall temperature values of the
igniter, when it operates at the respective heat flux
with the bulk temperature shown in the y-axis and the
respective measured heat transfer coefficient.
Figure 12.Values of the modeled ignition wall
temperature (red) and the igniter temperature (blue)
for the cases with 10%wt. ethanol in the fuel stream
and 0,7 [MWm-2
] heat flux from the igniter.
When the temperature reached from the igniter
exceeds the critical ignition wall temperature
calculated from the model ignition takes place. This
seems to be the case in both presented cases.
Nevertheless, the model is very sensitive on the data
used for the chemical kinetics of the reaction. The
values used are average literature values and have a
high uncertainty. Apart from the simplifications of
the model, this is the most significant source of
uncertainty for the calculated ignition wall-
temperatures. Fig.13 shows an example of the
sensitivity of the model on the chemical kinetics data.
On this figure the ignition results are shown for the
case presented in Fig.11 with two different activation
energy values inside the uncertainty interval reported
from Mercadier (Mercadier 2007). In the case of
higher activation energy, the bulk temperature must
be at least 380°C, for ignition to occur with the
shown heat flux from the igniter.
It is apparent, that the presented model is a
qualitative approximation and its quantitative results
must be interpreted very carefully.
Figure 13. Activation energy sensitivity of the
ignition conditions for the case shown on Fig.12 @
40 [kghr-1
]
CONCLUSION
A simple and robust ignition system has been
developed for hydrothermal flames. Voltage values
of 230 V could be fed to a ceramic igniter at 260 bar
and 400°C. The heat transfer conditions have been
characterized in the burning chamber, where the
ignition experiments will be carried out.
The measurement of the convective heat transfer
coefficient in the burner setup was the first step of the
assisted ignition project in our pilot plant. Based on
the performed measurements, a set of operational
points of the plant will be chosen and ignition
experiments will be performed for these points.
Additionally a simple model for the hot surface
ignition has been adapted to the hydrothermal flames
case and the ignition conditions have been calculated.
The results of the model show, that ignition will most
probably be possible with the current setup.
Aim of the ignition project is to have a reliable
ignition source, which will allow for the easy ignition
of hydrothermal flames in our plant. The
investigations performed in this project will be very
useful input for applications in real boreholes,
because many aspects of the assisted ignition of
hydrothermal flames will be solved. Data, like the
ignition temperature and the respective heat flux
values for specified operational conditions of a flame
are valuable input for the dimensioning of an
industrial igniter for hydrothermal flames.
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